This is a bit of a cheat, because it's not a horror movie about a terrifying fictional threat, but a terrific made-for-television movie about what happened the night millions of American's mistook a terrifying fictional threat for the actual end of the world.
In other words, the first case of widespread panic caused by Fake News.
It was October of 1938, the airwaves were full of dire and unbelievable accounts from Europe of Nazi invasions and conquest, and the boys and girls of Orson Welles' Mercury Theater group were looking for a way to juice-up H.G. Wells' "The War of the Worlds" for the radio so that it didn't sound like a museum piece. And that's when Orson Welles came up with the idea of using the kind of radio everyone was hearing already -- live, breaking news -- and staging "The War of the Worlds" as if it were news that was unfolding at that moment: news which at first lightly interrupted and then overtook the "actual" broadcast.
Which scared the crap out of a million people who didn't hear the beginning of the show, didn't read the announcement in the paper explaining what the show would be about, and never thought to change the channel and see how other broadcast networks were handling the end of the world.
I'm sure there's a lesson in there somewhere, but for now, enjoy!
Also for your viewing pleasure, there is also a documentary/re-creation of the events of that evening here and a shorter, black-and-white movie about the same events from 1957 -- "The Night America Trembled" -- starring Warren Beatty, Ed Asner, Warren Oates, James Coburn, Vincent Gardenia, and John Astin.